On Subgroups of Coxeter Groups

Abstract

The virtual cohomological dimension of a finitely generated Coxeter group G over a ring R is finite and known. We characterize the infinitely generated Coxeter groups of finite vcd, we give Coxeter groups that are virtual Poincare duality groups over some rings but not over others, and we exhibit a group whose vcd over the integers is three whereas its vcd over any field is two. We also give explicit presentations and Eilenberg-Mac Lane spaces for some of Bestvina's examples of groups whose vcd depends on the choice of ring.